Mouth
To make the mouth you put your hook from front to back and pull a loop of yarn through. You then move to the next hole and put the hook from front to back and pull a loop through the hat and the loop you have on the hook.

Carry on till you make the shape of a mouth.
Attach everything to the hat

As you can see you keep repeating row 4 (3 times) and then row 2 (3 times) to create the basket weave I completed 42 rows and then finished.
Once you have finished you are left with a rectangle and you just need to sew up the side & bottom edge.

If you are making a cozy for a specific mug check sizing as you go You might not need to do as many rounds 1-6 (if you want to make the bottom smaller) & you might not need as many rounds up for the height 9 – 14.

Ch 2

Round 1)8 htr in 2nd ch from hk, ss to join (8)

Round 2)Ch 2, 1 htr in same st, 7 htr inc, ss to join to top of the ch 2 (16)